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Lecture 21
Neutron stars
Neutron stars
If a degenerate core (or white
dwarf) exceeds the Chandrasekhar
mass limit (1.4MSun) it must collapse
until neutron degeneracy pressure
takes over.
M  1.4M Sun
R  10km
  6.65 1017 kg / m3  2.9  nuclear
Neutron stars
M  1.4M Sun
R  10km
  6.65 1017 kg / m3  2.9  nuclear
The force of gravity at the surface is very
strong:
GM
g  2  1.8 1012 m / s 2
R
• An object dropped from a height of 1 m would hit
the surface at a velocity 0.6% the speed of light.
• Must use general relativity to model correctly
Creation of Neutrons
• Neutronization: At high densities, neutrons are created rather
than destroyed
 The most stable arrangement of nucleons is one where neutrons and
protons are found in a lattice of increasingly neutron rich nuclei:
56
26
62
28
64
28
86
36
118
36
Fe, Ni, Ni, Kr,..., Kr
• This reduces the Coulomb repulsion between protons
Neutron Drip
• Nuclei with too many neutrons are unstable; beyond the
'neutron drip-line', nuclei become unbound.
 These neutrons form a nuclear halo: the neutron density
extends to greater distances than is the case in a well-bound,
stable nucleus
Superfluidity
• Free neutrons pair up to form bosons
 Degenerate bosons can flow without viscosity
 A rotating container will form quantized vortices
• At ~4x1015 kg/m3 neutron degeneracy pressure dominates
 Nuclei dissolve and protons also form a superconducting superfluid
Neutron stars: structure
1. Outer crust: heavy nuclei in a fluid ocean or solid lattice.
2. Inner crust: a mixture of neutron-rich nuclei, superfluid
free neutrons and relativistic electrons.
3. Interior: primarily superfluid neutrons
4. Core: uncertain conditions; likely consist of pions and other
elementary particles.
•
The maximum mass that can
be supported by neutron
degeneracy is uncertain,
but can be no more than
2.2-2.9 MSun (depending on
rotation rate).
Rotation
Conservation of angular momentum led to the prediction that
neutron stars must be rotating very rapidly.
Cooling
Luminosity (ergs/s)
Surface temperature (K)
• Internal temperature drops to ~109 K within a few days
• Surface temperature hovers around 106 K for about
10000 years
Neutron stars: luminosity
What is the blackbody luminosity of a 1.4 MSun neutron
star, with a surface temperature of 1 million K?
Chandra X-ray image of a
neutron star
Break
Pulsars
• Variable stars with very well-defined periods (usually 0.252 s).
• Some are measured to ~15 significant figures and rival the
best atomic clocks on earth
Pulsars
• The periods increase very gradually, with
 Characteristic lifetime of ~107 years.
dP
 10 15
dt
Pulsars
Pulsar PSR1919+21
• The shape of
each pulse shows
substantial
variation, though
the average pulse
shape is very
stable.
time
Possible explanations
How to obtain very regular pulsations?
1.
Binary stars: Such short periods would require very small
separations.
•
Could only be neutron stars. However, their periods would decrease
as gravitational waves carry their orbital energy away.
2. Pulsating stars
•
•
White dwarf oscillations are 100-1000s, much longer than observed
for pulsars
Neutron star pulsations are predicted to be more rapid than the
longest-period pulsars.
3. Rotating stars
•
How fast can a star rotate before it breaks up?
Pulsars: rapidly rotating neutron stars
•
•
Discovery of the pulsar in the Crab nebula in 1968 (P=0.0333s)
confirmed that it must be due to a neutron star.
Many pulsars are known to have high velocities (1000 km/s) as expected
if they were ejected from a SN explosion.
Pulsar model
• The model is a strong dipole magnetic field, inclined to the rotation
axis.
• The time-varying electric and magnetic fields form an EM wave
that carries energy away from the star as magnetic dipole
radiation.
• Electrons or ions are propelled from the strong gravitational field.
As they spiral around B-field lines, they emit radio radiation.
• Details are still very much uncertain!
The Crab Pulsar
• This movie shows dynamic rings, wisps and jets of matter
and antimatter around the pulsar in the Crab Nebula
1 light year
X-ray light (Chandra)
Optical light (HST)
Crab nebula: energy source
• We saw that the Crab nebula
is expanding at an
accelerating rate. What
drives this acceleration?
• To power the acceleration of
the nebula, plus provide the
observed relativistic
electrons and magnetic field
requires an energy source of
5x1031 W.
M  1.4 M Sun
R  10 4 m
P  0.0333s
P  4.2110 13
Tests of General Relativity
• PSR1913+16: an eccentric binary pulsar system
 Can observe time delay as the gravitational field increases and
decreases
 Curvature of space-time causes the orbit to precess
 Loss of energy due to gravitational waves
Shapiro Delay
• When the orbital plane is along the line of sight, there
is a delay in the pulses due to the warping of space